Heat oven to 350°F. Grease and flour two 9 x 2-inch round cake pans.
Melt chocolate in small bowl over hot, not boiling, water; cool.
Sift together flour, baking soda and salt onto waxed paper.
Beat butter in bowl until soft. Beat in sugar and eggs at high speed until light and fluffy, 5 minutes. Beat in vanilla and melted chocolate.
Stir in flour mixture alternately with sour cream, beating with wooden spoon after each addition until smooth. Stir in boiling water (batter will be thin). Divide at once between prepared pans.
Bake in 350°F oven 35 minutes or until centers spring back when lightly pressed with fingertips. Cool layers in pans on wire rack, 10 minutes. Loosen around edges with small knife or spatula; turn out onto wire racks and cool completely.
Meanwhile, prepare Chocolate Fudge Frosting (recipe follows).
Place one cake layer on a large serving plate. Spread with about one-quarter of the frosting. Place the second layer on top. Spread the remaining frosting over the sides and top of the cake.
Combine unsweetened chocolate and butter in a small heavy saucepan. Place the pan over low heat just until melted, stirring occasionally. Remove from heat. Combine powdered sugar, milk and vanilla in a medium-size bowl; stir together until smooth. Stir in the chocolate mixture until well blended. Set the bowl in a pan of ice water and beat with a wooden spoon until the frosting is thick enough to spread and hold its shape.